The present disclosure relates to LED light sources, particularly to such sources that include encapsulants, lenses, films, and the like that are shaped or otherwise configured to redirect light propagating initially along a light emitting axis into other directions. The resulting optical assembly is particularly useful, whether singly or in an array, in flat illumination sources (e.g., room lights), in backlights for liquid crystal display (LCD) devices and the like, such as TVs, computer monitors, personal digital assistants (PDAs), mobile telephones, and so forth.